can you add an image to show what this is about? next: ANY weird behaviour regarding artifacts should be a -bug-. So best option would be to file a bug against the corresponding package
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RinzwindApr 19 '14 at 12:43

I tried both suggestions of adding the -bs as well as enabling that libsdl ppa and neither made my screen tearing go away. Playing minecraft I have major screen tearing when running up and down stairs. I am using a GTX 760 with Nvidia Binary BLOB 337.25. VSync is enabled within the game. Sync to VBlank is also enabled within the nvidia-settings so if anyone else has any other suggestions please let me know, this screen tearing is driving me through the roof!
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Ubu the Tech GuruMay 31 '14 at 21:02

Just to sum up to the Brenden's answer, the real problem is with the libsdl1.2 package, as stated in this bug report.

The solution is ready, but somehow isn't available on default Ubuntu package sources yet (at least not for me). So, a way to solve this is to import the developer PPA and install the patched package directly:

Screen tearing can also be caused by xfce compositing or window manager with compositing that doesn't suppport vblank sync! To fix the issue i used compton, which completely stops the tearing, it's also quite easy to configure, i followed this guide and i haven't had any problems.

I stumbled across this query whilst looking for solutions to the same problem with my AMD hybrid card (Radeon HD 8650G) and thought I'd drop an answer for others arriving here for the same reason.. I've managed to get all the proprietary drivers downloaded from AMD to run on Trusty, but the tearing has always remained present. The only version that has worked for me is to install the experimental drivers which have a 'tear free' page which works. The version is fglrx-14.20 which is packaged as

linux-amd-catalyst-14.6-beta-v1.0-jul11.zip

The latest stable release of fglrx - 14.301.1001 does not have the 'tear free' page and does not stop the tearing. A downgrade to 14.20 brought back the desired behaviour in both video playback and games. Hope this helps.